THE JOURNAL OF CHEMICAL PHYSICS 122, 204307 共2005兲
Ab initio potential-energy surface for the reaction Ca+ HCl\ CaCl+ H
Gilles Verbockhaven
Institute of Theoretical Chemistry, Institute for Molecules and Materials (IMM), University of Nijmegen,
Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
Cristina Sanz
Institute of Theoretical Chemistry, Institute for Molecules and Materials (IMM), University of Nijmegen,
Toernooiveld 1, 6525 ED Nijmegen, The Netherlands and Instituto de Matemáticas y Física
Fundamental, Consejo Superior de Investigaciones Científicas (CSIC), Serrano 123, 28006 Madrid, Spain
Gerrit C. Groenenboom
Institute of Theoretical Chemistry, Institute for Molecules and Materials (IMM), University of Nijmegen,
Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
Octavio Ronceroa兲
Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas (CSIC),
Serrano 123, 28006 Madrid, Spain
Ad van der Avoirdb兲
Institute of Theoretical Chemistry, Institute for Molecules and Materials (IMM), University of Nijmegen,
Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
共Received 17 December 2004; accepted 8 March 2005; published online 23 May 2005兲
The potential-energy surface of the ground electronic state of CaHCl has been obtained from 6400
ab initio points calculated at the multireference configuration-interaction level and represented by a
global analytical fit. The Ca+ HCl→ CaCl+ H reaction is endothermic by 5100 cm−1 with a barrier
of 4470 cm−1 at bent geometry, taking the zero energy in the Ca+ HCl asymptote. On both sides of
this barrier are potential wells at linear geometries, a shallow one due to van der Waals interactions
in the entrance channel, and a deep one attributed to the H−Ca++Cl− ionic configuration. The
accuracy of the van der Waals well depth, ⬇200 cm−1, was checked by means of additional
calculations at the coupled-cluster singles and doubles with perturbative triples level and it was
concluded that previous empirical estimates are unrealistic. Also, the electric dipole function was
calculated, analytically fitted in the regions of the two wells, and used to analyze the charge shifts
along the reaction path. In the insertion well, 16 800 cm−1 deep, the electric dipole function
confirmed the ionic structure of the HCaCl complex and served to estimate effective atomic charges.
Finally, bound rovibrational levels were computed both in the van der Waals well and in the
insertion well, and the infrared-absorption spectrum of the insertion complex was simulated in order
to facilitate its detection. © 2005 American Institute of Physics. 关DOI: 10.1063/1.1899154兴
I. INTRODUCTION
Chemical reactions involve a drastic change in the electronic structure from reactants to products. Harpoonlike reactions between metal atoms 共M兲 and halide molecules 共XR
with X = F, Cl, Br, or I and R = H or CH3兲 constitute nice
examples of such reordering: one electron of the metal atom
“jumps” towards the halide molecule and forms an unstable
anion, which fragments and leads to products MX and R. The
XR and MX systems are polar and possess strong electronic
and vibrational transition dipole moments, so one may use
the photon excitation of reactants and products to study the
influence of electronic, vibrational, and rotational excitations
of reactants, the final-state distribution of products, and the
stereodynamics. In addition, the interaction between the reactants gives rise to van der Waals complexes that can be
used to spectroscopically examine the transition state dynama兲
Electronic mail: [email protected]
Electronic mail: [email protected]
b兲
0021-9606/2005/122共20兲/204307/12/$22.50
ics after the electronic excitation of the metal atom. A recent
review by Mestdagh et al.1 provides a comprehensive description of the reaction dynamics of these systems.
The harpoon mechanism was first studied for systems in
which M is an alkali-metal atom.2 These systems are relatively simple because the metal cation M + and the halogen
anion X− are both closed-shell systems, so that the first excited electronic state of the MX product 共or rather M +X−,
since it is ionic兲 is extremely high in energy and only the
ground electronic state of the products is of interest. Many
experimental studies on the reactive collisions of these systems have been performed.1,2 The system studied mostly
from a theoretical point of view is Li+ HF 共Ref. 3–8兲 because its number of electrons is relatively low, which allows
accurate ab initio calculations. The experimental electronic
spectra recorded for some of these systems, such as Na–HF
共Ref. 9兲 and Li–HF,10 have been nicely reproduced by theoretical calculations.11–14 The bound levels in the excited electronic states decay through electronic predissociation. In the
122, 204307-1
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J. Chem. Phys. 122, 204307 共2005兲
Verbockhaven et al.
case of Li–HF this process leads mainly to LiF products,15
whereas for Na–HF it seems that only a negligible amount of
NaF products is formed.16,17
The situation for alkali-earth atoms is far more complicated, because the M + cation is an open shell system in this
case. The energy curves of the M +共 2S , 2D , 2 P兲 + RX− ionic
states intersect with those of the M共 1S , 1D , 1 P兲 + RX covalent
states, determining the regions where the electron jumps
from the metal to the halide. The different crossings yield the
MX product in particular states, X 2⌺ , A 2⌸, or B 2⌺. The
excited MX products are chemiluminescent, and the analysis
of their spectra provides information about the product state
distribution and makes the experimental study of such reactions very attractive.
One of the best studied systems is Ca+ HCl. The reaction
Ca+ HCl→ CaCl+ H is highly endothermic, and it has been
studied with excited Ca共 1D , 1 P兲 atoms.18–26 It was found22
that when the excited Ca 4p orbital is aligned perpendicularly to the direction of approach to HCl the production of
CaCl in the A 2⌸ electronic state is enhanced, whereas a
parallel alignment favors the production of CaCl in the B 2⌺
state. Such a correlation was explained by assuming that the
p orbital of the excited Ca atom transforms into a CaCl molecular orbital.22 The fact that the A / B branching ratio depends only weakly on the Ca p orbital alignment was attributed to the presence of a dominant channel towards the
CaCl共X 1⌺兲 ground state. Because some of the potential
crossings seem to occur at long distances, they are mainly
affected by the long-range behavior of the ionic and covalent
potential surfaces. Models of such crossings qualitatively explain this A / B ratio dependence27 and, moreover, lead to a
quantitative understanding of the energy dependence of the
Ca共 1D兲 + HCl reactive cross sections.28 However, these models are based on long-range interactions and introduce ad hoc
parameters to fit the experimental results. Ab initio calculations of the multiple crossings are therefore necessary to get
a deeper insight in these reactions.
An alternative experimental study on the reaction dynamics of this system has been made by photon excitation of
the Ca atom in the Ca共 1S兲 − HCl van der Waals complex.29–32
In a covalent picture the excited states correlate to Ca共 1D兲
and Ca共 1 P兲. For the case of Ca共 1 P兲 − HCl, the electrostatic
interaction yields one A⬘ state with a linear equilibrium geometry, similar to the ground state of the complex, and two
other states of A⬘ and A⬙ symmetries with a T-shaped equilibrium geometry.33 This situation explains the redshift and
blueshift features of the Ca–HCl spectrum relative to the
Ca共 1 P ← 1S兲 transition. The nonreactive electronic relaxation
channels yielding Ca共 1S , 1 P兲 + HCl fragments are analyzed
but were not observed. The dominant processes are either
slow vibrational predissociation or electronic predissociation. The electronic predissociation is considered less probable since it is due to couplings between covalent states and
those states do not intersect. By contrast, the ionic channels,
associated with the formation of CaCl products, cross with
the initially populated Ca共 1D , 1 P兲 − HCl covalent states,
which explains why these channels become dominant. The
CaCl product was initially not detected in its electronic
ground 共X兲 state either,29–31 its detection being particularly
difficult because of vibrationally cold CaCl共X兲 produced in
the process of formation of the van der Waals complex.
Later, the vibrational state distribution of CaCl共X , ␷兲 was
observed32 with a maximum as high as ␷ = 30 and extending
up to ␷ = 60. This unusually excited vibrational distribution
explains the difficulties in detecting CaCl共X兲, and confirms
that this fragmentation channel involving the ground adiabatic electronic state of the system is important.
Although the long-range interaction models applied to
the ground as well as to the excited states27,28,31,33 are partly
based on ab initio data, there is no accurate ab initio calculation of the ground electronic state of CaHCl. The only
available potential surface is based on a diatoms-inmolecules 共DIMs兲 model34 for collinear geometries. This
model predicts a rather shallow HCaCl insertion well. This
well is, however, much deeper in other related systems such
as Ca–HF,35 Mg–HF,36 Sr–HF,37 and Be–HF.38 It is assumed
that the well is artificially shallow in the DIM model because
the contribution of the H−Ca2+Cl− configuration, among others, is not considered. This will be discussed below.
The aim of this work is the accurate ab initio calculation
of the ground-state potential-energy surface, from Ca+ HCl
reactants to CaCl+ H products, passing through the van der
Waals and insertion wells. The first well is important in
studying the photoinduced reaction dynamics for the excited
states of Ca, while the second should be very important in
determining the insertion mechanism in the reaction dynamics. The huge difference in well depth between the two wells
introduces difficult problems in the ab initio calculations as
well as in fitting the surface, as will be described below. The
electronic properties of the states that produce the potential
surface change along the reaction path because of multiple
electron jump mechanisms. This will be analyzed by studying the electric dipole expectation value. Moreover, the dipole moment function allows the study of infrared transitions
and the simulation of the spectrum obtained from the insertion well.
II. AB INITIO CALCULATIONS
The potential-energy surfaces were computed using the
2000 quantum chemistry package developed by
Werner et al.39 Two different methods were used. Ground
and excited electronic states of the Ca atom and the full
three-dimensional CaHCl ground-state potential surface for
the chemical reaction were computed by the multireference
configuration-interaction 共MRCI兲 method with orbitals and a
reference space obtained from complete active space selfconsistent-field 共CASSCF兲 calculations. The potential of the
Ca–HCl van der Waals well in the entrance channel—the
only channel involving two closed-shell entities—was also
computed 共for fixed H–Cl bond length兲 by the coupledcluster method with single and double excitations and perturbative triples 关CCSD共T兲兴 and orbitals obtained from Hartree–
Fock 共HF兲 calculations. This method is most suitable for
weak van der Waals interactions comprising predominantly
dispersion forces.
Special attention was given to the choice of the atomic
basis functions. In a recent paper, Leininger and Jeung40 reMOLPRO
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204307-3
J. Chem. Phys. 122, 204307 共2005兲
Potential-energy surface for Ca+ HCl
TABLE I. Comparison of calculated excitation energies ⌬E 共in cm−1兲 and
oscillator strengths gf of the 1 P ← 1S and 1D ← 1 P transitions in Ca with
experimental and literature data.
1
Experimenta
b
d
1
P
De共cm−1兲
D
⌬E
gf
⌬E
gf
Method
RHCl−Ca共Å兲
No CP
CP
23 652
23 762
23 979
1.79共3兲
1.67c
21 849
22 576
24 316
0.0051共14兲
0.006c
MRCI
MRCIa
CCSD共T兲
5.156
5.158
5.011
−189.5
−187.2
−229.5
−176.4
−174.1
−218.5
a
Excitation energies from Ref. 63, oscillator strengths from Refs. 64–66 for
the 1 P ← 1S and 1D ← 1 P transitions, respectively.
b
Reference 40.
c
The gf values with the basis of Leininger and Jeung were computed by us.
d
References 27,42.
ported the excitation energy of the 4s4p共 1 P兲 and 3d4s共 1D兲
states of the Ca atom to show the quality of their calcium
basis. The basis set is built on Wachters’ 14s11p5d Gaussiantype orbital basis.41 The 15s13p5d Gaussians were optimized
on the 4s2共 1S兲, 4s4p共 3 P兲, and 3d4s共 3D兲 states. One diffuse s
and one diffuse d orbital were added before the contraction
into a 12s9p5d atomic basis, while two added f orbitals remain uncontracted. With this basis we performed MRCI calculations on the Ca atom including valence and core-valence
correlations; the active space consisted of the 3s , 3p , 4s, and
4p orbitals. The errors in the excitation energies of the 1 P
and 1D states are only about 100 and 750 cm−1,
respectively40 共see Table I兲. This is smaller than the
errors found with other bases, such as those reported by
Meijer et al.27,42 As reported in Table I, the 4s2共 1S兲
→ 4s4p共 1 P兲 oscillator strength agrees with experiment to
within 10%. This justifies the choice of this basis for the
present work. Once the basis for Ca was chosen, the Ca–HCl
ground-state van der Waals minimum was computed with the
MRCI method using different augmented correlation consistent basis sets for H and Cl. The results, listed in Table II,
show that the binding energy of the Ca–HCl complex is converged with respect to the one-electron basis to within
1 cm−1 with the augmented correlation consistent polarized
valence triple zeta43 共aug-cc-pVTZ兲 and the augmented correlation consistent polarized valence quadruple zeta44 共augcc-pVQZ兲 bases for H and Cl, respectively. These bases were
chosen in all further calculations.
The global three-dimensional CaHCl potential-energy
surface was computed using large scale internally contracted
MRCI calculations with orbitals optimized by a CASSCF
procedure. Core-core and core-valence correlations in the Ca
atom were neglected in order to improve the stability of the
CASSCF and MRCI procedures. In the CASSCF, as well as
TABLE II. Van der Waals well depth De 共in cm−1, without CP correction兲
from MRCI calculations with different basis sets. The basis of Ref. 40 is
used for Ca.
H \ Cl
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
TABLE III. MRCI and CCSD共T兲 results for the equilibrium distance and
depth De of the Ca-HCl van der Waals minimum, without and with CP
correction.
aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z
¯
227.3
228.8
229.7
166.4
196.9
197.6
197.6
161.9
189.5
189.6
189.6
161.4
189.7
189.7
189.7
a
From the global fit.
in the MRCI calculations the active set was restricted to the
molecular orbitals correlating with the 3s and 3p orbitals of
Cl, the 4s and 4p orbitals of Ca, and the 1s orbital of H. This
choice was motivated by the mixing between the 4s2 and 4p2
configurations found for the Ca ground state: a ratio of 13 is
to 1 is reported by Hansen et al.45 Using this active space,
616 configuration state functions 共CSFs兲 are included in the
CASSCF calculations, while the MRCI is based on the same
616 reference configurations. For a more accurate description
of the diatomic limits involved in the present work, one
would need to open the Ca core 共see below兲. In order to
correct the MRCI energies for size inconsistency we applied
the so-called Davidson 共Q兲 correction.46
For the weakly bound Ca–HCl entrance channel complex the accuracy of the MRCI procedure was tested by performing CCSD共T兲 calculations with the same basis. Table III
shows a comparison of the results. The Boys and Bernardi47
counterpoise 共CP兲 method was used to correct the Ca-HCl
binding energy for the basis set superposition error 共BSSE兲
in both MRCI and CCSD共T兲 calculations. The CP correction
is the difference between the sum of the energies of the Ca
and HCl monomers computed in the full Ca–HCl dimer basis
and the sum of the monomer energies computed in the respective monomer bases. It was found that the maximum CP
correction for RCa−HCl 艌 4.5 Å is on the order of 15 cm−1 for
CCSD共T兲, as well as for MRCI. The binding energy of the
weakly bound complex is reduced by about 5% by this correction. The definition of CP corrections for the product
channel and especially in the reaction zone is not straightforward. Therefore, and because of the small size of the corrections found for the entrance channel, the CP correction was
not applied in the calculations of the global potential surface.
The global potential was calculated on a grid of more
than 6000 geometries that consists of three 共overlapping兲
smaller grids, each described by a set of valence coordinates.
Most points were computed on the grid with the valence
coordinates given by the Ca–Cl bond length, the Cl–H bond
length, and the Ca–Cl–H angle. The Ca–Cl bond length was
varied from 4 to 12a0, the Cl–H bond length from 2.2 to 8a0,
and the Ca–Cl–H angle from 0 to 180°, mostly in steps of
15°. The step size in the bond lengths was chosen smaller
close to the equilibrium geometry. The other two grids on
which supplementary points were generated were in
H–Ca–Cl and Ca–H–Cl valence coordinates.
A separate grid of about 330 points was chosen for the
MRCI and CCSD共T兲 calculations on the Ca–HCl entrance
channel complex, i.e., in the region of the van der Waals
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204307-4
J. Chem. Phys. 122, 204307 共2005兲
Verbockhaven et al.
well. The H–Cl distance was frozen at its experimental equilibrium value of 1.2746 Å.48 The Ca–Cl–H valence angle
was varied between 0° and 180° in steps of 15° and the
Ca–Cl distance ranged from 3.5 to 25a0. In total the energy
was computed for about 6400 points.
It was mentioned above that the size of the active space
in the CASSCF calculations and the number of the electrons
that are explicitly correlated had to be restricted in order to
ensure convergence of the CASSCF calculations. One of the
reasons for the convergence problems is that the covalent
and ionic potential surfaces have multiple crossings, responsible for the harpooning effect. When the covalent and ionic
surfaces are very close to each other the CASSCF procedure
may converge towards the higher surface and thus find a
metastable solution, while a stable solution exists at lower
energy. In addition, the CASSCF procedure sometimes converges to metastable solutions which do not have any physical meaning. In regions where such computational annoyances were observed both the covalent and ionic solutions
were calculated. The orbitals were more or less forced to
have the desired character by starting from a purely covalent
or ionic initial guess. This was also a reason for making the
three grids overlap; approaching a point from different directions sometimes produced different converged solutions. It
was ensured that the results obtained in the end were always
consistent, but it was sometimes difficult to obtain adequate
initial guesses.
Although the calculations were performed on a grid described by three sets of valence coordinates we used Jacobi
coordinates associated with the different reaction channels in
dynamical calculations. The Ca+ HCl reactant Jacobi vectors
are the vector RHCl–Ca from the HCl center of mass to the Ca
atom, and the vector rCl–H from the Cl to the H nucleus. The
lengths of these vectors are RHCl–Ca and rCl–H and the Jacobi
angle ␪ is the angle between them. The CaCl+ H product
Jacobi vectors RCaCl−H and rCl–Ca are defined analogously,
and the angle between these vectors is denoted by ␥.
III. FITS AND CHARACTERISTICS OF THE POTENTIAL
SURFACE
In order to use the potential-energy surface in dynamical
calculations the ab initio points described above were fitted
by analytical functions. Two fit procedures were applied: a fit
to the complete set of 6400 points computed by MRCI on the
global grid and a local fit in the region of the van der Waals
well to the extra points calculated in the entrance channel.
This local fit was applied both to the MRCI and CCSD共T兲
results and it was used to check the accuracy of the global fit
in the weak-interaction region.
A. Global fit
We used a fit procedure developed by Aguado and
co-workers,7,49 but some modifications50 were required. The
original procedure starts from a many-body expansion of the
potential of three interacting atoms A , B, and C
VABC = V共3兲共RAB,RAC,RBC兲 +
共2兲
共RAB兲.
兺 VAB
共1兲
A⬍B
共2兲
The sum of the atomic energies is first subtracted, the VAB
are
共3兲
the pair energies, and VABC is the three-body energy. The pair
energies are expressed in terms of short and long-range contributions
共2兲short
= cAB
VAB
0
exp共− ␣ABRAB兲
RAB
共2兲
N
共2兲long
VAB
=
i
cAB
兺
i ␳AB ,
i=1
where ␳AB = RAB exp共−␤ABRAB兲 and N is the order of the
polynomial in the long-range term. The three-body term is
expressed as a polynomial of order M, the maximum of
i + j + k, in the variables ␳AB , ␳AC, and ␳BC
M
V共3兲共RAB,RAC,RBC兲 =
i
j
k
dijk␳AB
␳AC
␳BC
.
兺
i,j,k
共3兲
In the standard procedure the pair energies are first fitted
to obtain diatomic potential curves of the form of Eq. 共2兲,
while the three-body contribution is found by subtracting the
sum of the pair energies from the total interaction energy,
and then fitted to Eq. 共3兲. In the case of CaHCl this did not
work well; the problem is related to the fact that each of the
diatomic fragments shows an ionic/covalent crossing when
the internuclear distance increases, which produces ionic/
covalent crossings also in the global surface. Very high-order
terms were needed in the fit of the three-body potential obtained after subtraction of the pair interactions and artificial
oscillations appeared. Also, the usual procedure to represent
curve crossings by diagonalizing a 2 ⫻ 2 matrix did not produce satisfactory fits, probably because multiple ionic states
are involved 共see below兲. So we used a modified version of
the standard procedure in which the pair and three-body
terms are fitted simultaneously and the pair terms have the
form of the terms in the three-body energy with two of the
exponents, i , j , k equal to zero. This implies that only the
polynomial pair terms defined in Eq. 共2兲 were included, but
one should remember that these terms contain the variables
␳AB that depend exponentially on the interatomic distances
RAB. Instead of a single three-body term we used two such
共L兲
共L兲
共L兲
terms, with different exponents ␤AB
, ␤AC
, and ␤BC
in the
共L兲
共L兲
共L兲
variables ␳AB , ␳AC, and ␳BC with L = 1, 2
2
VABC =
共L兲 共L兲 共L兲
, ␳AC, ␳BC兲.
VL共3兲共␳AB
兺
L=1
共4兲
Each of the terms VL共3兲 has the form of Eq. 共3兲 with polynomials of order N = 8 in the pair terms that have two of the
indices i , j , k equal to zero and order M = 5 in the real threebody terms. This gave a satisfactory representation of all the
points on the global grid with no oscillations.
A feature of the potential that could not be reproduced
with the original fitting procedure is the van der Waals well
in the entrance channel. This minimum is about 80 times
shallower than the global insertion minimum, which makes
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J. Chem. Phys. 122, 204307 共2005兲
Potential-energy surface for Ca+ HCl
TABLE IV. Root-mean-square deviation 共rmsd, in cm−1兲 of the global fit
from the calculated MRCI ab initio points. The energy is relative to the
Ca+ HCl asymptote with HCl at its equilibrium distance; Ngeom is the number of geometries within the given energy range.
TABLE V. Stationary points on the CaHCl ground-state potential-energy
surface 共distances in Å and energies in cm−1兲. Valence coordinates are used
in this table.
Coordinates
Energy range
Ngeom
rmsd
E ⬍ 100 000
50 000⬍ E ⬍ 100 000
25 000⬍ E ⬍ 50 000
10 000⬍ E ⬍ 25 000
0 ⬍ E ⬍ 10 000
−10 000⬍ E ⬍ 0
−17 000⬍ E ⬍ −10 000
−200⬍ E ⬍ 100
6752
61
826
1965
2818
838
243
307
561
794
862
663
429
299
266
5
Stat. point
its representation very difficult. It has been shown51,52 that
the inclusion of extra three-body terms was useful to better
describe the long range of the potential. The modified procedure applied here contains such terms and gives a good fit of
the van der Waals well.
The root-mean-square error in the final fit is 561 cm−1,
but it is more illustrative to look at specific errors in different
regions of the potential surface. These are listed in Table IV.
The last row of this table shows the good quality of the
global fit for the van der Waals well in the entrance channel.
The major features of the surface are shown in the minimumenergy path in Fig. 1, the stationary points are given in
Table V. Figure 2 shows contour plots of the global
potential-energy surface for different values of the Ca–Cl–H
angle chosen to illustrate the features near the stationary
points listed in Table V. The full set of ab initio data and the
code that generates the fitted potential can be obtained from
the authors upon request.
In Table VI the dissociation limits of the global potential
are compared with experimental data for the diatomic molecules to estimate the accuracy of the MRCI procedure. The
difference between De computed from the fit and from the ab
initio points is less than 6% for CaH, less than 2% for HCl,
and about 1% for CaCl. Those values show that the fit in the
regions close to the dissociation limits is accurate. Two dissociation energies are found to be overestimated 共for HCl
and CaH兲 and one is underestimated 共for CaCl兲, which implies that the discrepancies cannot be explained by a systematic error in the description of the Ca or Cl atom. The equilibrium distances computed for CaCl and CaH are larger by
FIG. 1. Overview of the minimum-energy path for the Ca+ HCl→ CaCl
+ H reaction and the energies of relevant excited states.
Reactants
vdW minimum
Transition state
Global minimum
Products
RCa–Cl
RH–Cl
H-Cl–Ca angle
Energy
⬁
5.194
2.691
2.524
2.500
1.282
1.268
1.582
4.591
⬁
¯
0°
56°
0°
¯
0
−187
4468
−16 852
5101
0.06 Å than the experimental values, while the H-Cl bond
length is reproduced very well. This overestimate of the bond
length is a consequence of the fact that the core-core and
core-valence correlations in the Ca atom were neglected in
order to keep the CASSCF and MRCI procedures stable over
the whole surface. Hansen et al.45 have shown that the inclusion of core correlation leads to a contraction of the outer Ca
orbitals, which would reduce the molecular bond lengths of
CaH and CaCl.
The global minimum corresponds to a collinear geometry with the Ca atom inserted between H and Cl. The Ca–Cl
and Ca–H distances obtained from the fit are 2.52 and 2.07
Å, respectively, slightly larger than the diatomic bond
lengths in Table VI. From the ab initio points the minimum-
FIG. 2. Contour plots of cuts through the global potential-energy surface, as
function of the Ca+ HCl Jacobi coordinates. The contours are plotted for
energy intervals of 4000 cm−1, except for the cut at ␪ = 57° where the contour at 4000 cm−1 was replaced by a contour at 4470 cm−1 in order to show
the exact location of the transition state.
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204307-6
J. Chem. Phys. 122, 204307 共2005兲
Verbockhaven et al.
TABLE VI. Equilibrium distances Re 共in Å兲 and dissociation energies D0 and De 共in cm−1兲 for the three
diatomic limits of the CaHCl complex. Experimental data from Huber and Herzberg48.
Re
CaCl
CaH
HCl
a
De
This work
Expt.
This work
Theor.
2.500
2.065
1.282
2.439
2.002
1.275
32 835
15 175
37 936
14 428a
37 193c
D0
Expt.
This work
Expt.
32 990
14 425
32 650
14 503
36 397
32 988
13 711b
35 759
Semiempirical estimate 共Ref. 67兲.
This number corresponds to an upper limit.
Reference 68.
b
c
energy value is about −16 600 cm−1 and the CaCl and CaH
equilibrium distances are 2.59 and 2.12 Å, respectively. The
difference in De between the fit and the ab initio points is
only 200 cm−1, less than 1.5%. The occurrence of this deep
insertion well is due to the divalent character of the Ca atom.
The outer occupied CASSCF molecular orbitals show important Ca共4s兲 contributions in this region and have dominant H
or Cl character. We shall discuss this in more detail further
on. Similar calculations performed on related systems such
as Ca–HF,35 Mg-HF,36 Sr–HF,37 and Be–HF 共Ref. 38兲 also
produced a deep insertion well.
The insertion well is accessed from the Ca+ HCl entrance channel after surmounting a barrier. The saddle point
is at a bent geometry with ␪ = 57°. Such a bent transition
state is typical of these systems; it appears also for Ca–HF
共Ref. 35兲 and Mg–HF 共Ref. 36兲 and also in alkali–hydrogen
halide systems such as Li–HF.3,5,53 According to a DIM
model for Li− HX systems3 a resonance between two ionic
structures, Li+X −H and Li+H−X, is responsible for such a
bent transition state. This might be similar for systems containing alkali-earth atoms.
The H-Cl distance at the saddle point 共1.58 Å兲 is considerably larger than in the free HCl molecule 共1.28 Å兲. This
was also observed in the other systems mentioned above.
The origin of such a late barrier is an electron jump from Ca
to HCl, forming HCl−. Since HCl– is repulsive, the H–Cl
distance should increase in order to stabilize the Ca+ – HCl–
structure.
The saddle point is located at 4468 cm−1 above the Ca
+ HCl limit. The effective barrier decreases when the HCl
zero-point vibrational energy of 1540 cm−1 is considered.
The Ca+ HCl→ CaCl+ H reaction is endothermic by
5101 cm−1, which is more than the barrier height. The endothermicity is 3746 cm−1 when zero-point energies are
included.
B. van der Waals region
The shallow van der Waals well in the Ca–HCl entrance
channel deserves careful examination. It is of great interest
because the Ca–HCl complex is the precursor in the photoinitiated experiments of Soep and co-workers.29–32 They assumed a linear Ca–HCl equilibrium configuration of the
complex based on the geometries of known atom-HCl van
der Waals complexes as Hg–HCl.54 The present results, sum-
marized in Table V, also predict such a linear equilibrium
geometry with well depth De = 187 cm−1 according to the
global fit of the MRCI results.
The dissociation energy of the Ca–HCl complex was
estimated to be much higher: 1200± 400 cm−1 by Menéndez
et al.55 It was determined from the maximum internal energy
of the CaCl product observed in photoinitiated reactions,
with the assumption that the product recoil energy is negligible. Later on, de Castro-Vitores et al.23 reported an empirical potential with a binding energy of 980 cm−1 at an equilibrium distance of 4.14 Å. This estimate of the binding
energy assumed a contribution of van der Waals interactions
plus an important charge-transfer contribution. The well
depth based on van der Waals interactions alone was found
to be 210 cm−1, in fairly good agreement with the results
reported in this work.
It was already mentioned above that in addition to the
MRCI calculations CCSD共T兲 calculations were performed in
order to check the accuracy of the potential in the van der
Waals region. The CCSD共T兲 method, although not adequate
for the whole surface because it is based on a singleconfiguration reference wave function, is more suitable than
the MRCI method to compute the weak van der Waals interactions in the closed-shell Ca–HCl complex. The position
and depth of the well obtained with the two methods are
compared in Table III. The well depth from CCSD共T兲 calculations is about 40 cm−1 larger than the MRCI value, i.e.,
about 20%, and the equilibrium distance Re is about 3%
smaller. The CP corrections for the BSSE, also shown in
Table III, reduce De by about 5%. The best 共CP-corrected兲
value is De = 218 cm−1.
If there were an important charge-transfer contribution to
this well depth, it would have emerged from the MRCI and
CCSD共T兲 supermolecule calculations. We may therefore
conclude that the experimental estimate of the dissociation
energy by Menéndez et al.55 is much too high, so their assumption that the product recoil energy in the experiment
could be neglected is apparently not justified. The large discrepancy between the empirical estimate of de CastroVitores et al. and the present results originates from the
charge-transfer contribution, which was probably overestimated in Ref. 23.
With HCl frozen at its equilibrium bond length a local fit
of the potential in the van der Waals well region is performed
both for the MRCI and CCSD共T兲 results. Since the CP correction cannot be applied to the MRCI results for the global
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204307-7
J. Chem. Phys. 122, 204307 共2005兲
Potential-energy surface for Ca+ HCl
TABLE VII. Bound levels 共in cm−1兲 in the Ca–HCl van der Waals well of
the MRCI and CCSD共T兲 potentials for total angular momentum J = 0.
FIG. 3. Comparison between MRCI and CCSD共T兲 potentials for the entrance channel of the Ca+ HCl reaction in the corresponding Jacobi coordinates. Energies in cm−1, distance in Å, and angle ␪ in degrees.
potential we chose to use also the uncorrected MRCI and
CCSD共T兲 data in the local fit of the van der Waals well. The
interaction potential is written in the Ca–HCl Jacobi coordinates R ⬅ RHCl–Ca and ␪ and separated into long-range and
short-range terms, which are expanded as
6
Vshort =
9
兺 兺 dlpRp exp共− ␣R兲Pl共cos ␪兲,
p=0 l=0
14
Vlong =
9
兺 兺 clnR
n=6 l=0
−n
冋
Pl共cos ␪兲 1 − exp共− ␤R兲
共5兲
n
兺
k=0
册
共␤R兲k
,
k!
where Pl共cos ␪兲 are Legendre polynomials. The coefficients
cln , dlp, and the nonlinear parameters ␣ and ␤ were fitted in a
two-step procedure described in detail in Ref. 56. For the
region of interest, i.e., R 艌 4 Å, the largest difference between the ab initio energies and the fitted values, 0.3 cm−1,
was found in the repulsive region, for R = 4 Å and ␪ = 30°.
For larger R values the energies are reproduced within
0.05 cm−1.
The difference between the local fits performed on the
CCSD共T兲 and MRCI data can be observed in Fig. 3, where
they are also compared with the global fit. The global and
local fits of the MRCI points agree very well 共to within 2%兲,
v
MRCI
CCSD共T兲
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
−111.38
−90.46
−71.96
−65.46
−55.64
−49.30
−41.45
−35.28
−29.81
−28.68
−23.39
−19.22
−14.03
−12.41
−10.30
−6.74
−3.69
−0.13
−135.58
−111.00
−88.99
−72.15
−69.35
−55.45
−52.23
−40.58
−39.12
−37.43
−27.66
−25.09
−20.66
−17.41
−14.03
−9.80
−5.49
−4.54
−2.41
which confirms the accuracy of the method developed by
Aguado and co-workers7,49 to reproduce even small wells in
a global potential-energy surface.
A good test for comparing the two local fits obtained
from the CCSD共T兲 and MRCI points was the calculation of
the two-dimensional bound states in Ca–HCl Jacobi coordinates with the program TRIATOM.57 The number of radial
basis functions was 30 and the maximum j value in the angular basis was 20. The 共variationally optimized兲 nonlinear
parameters in the radial basis were Re = 9.47 and 9.74a0, De
= 212 and 190 cm−1, and ␻e = 6.8 and 6.8 cm−1 for the
CCSD共T兲 and MRCI potentials, respectively. The corresponding energy levels for total angular momentum J = 0 are
shown in Table VII. The dissociation energy D0 is considerably smaller than the well depth De. Also, the difference in
D0 with the CCSD共T兲 and MRCI potentials, 24 cm−1, is
smaller than the difference in De, which is ⬇40 cm−1. The
number of bound states with the two potentials differs only
by one. The first excited state is the intermolecular stretch
fundamental, and the second excited state has mostly bend
character. The stretch and bend frequencies are not very different in the two potentials. This similarity shows that also
the MRCI method, with a well-chosen basis, is able to describe the van der Waals region reasonably well. Combining
this conclusion with the previous one, we may end this section by summarizing that the global CaHCl potential-energy
surface obtained from the fit to the MRCI points gives a
fairly good representation of the van der Waals well.
IV. ELECTRIC DIPOLE MOMENT
The electric dipole surface serves to study infrared, i.e.,
rovibrational, transitions within the ground electronic state
that are of interest in this work. In addition, the electric dipole surface provides information about the electronic charge
distribution in the complex, which is of great interest for
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204307-8
J. Chem. Phys. 122, 204307 共2005兲
Verbockhaven et al.
electron around it. In HCaCl the highly polarizable electron
around the Ca++Cl core is transferred to the H atom, thus
producing a very stable ionic H−Ca++Cl− species. Finally,
when the product region is approached, the H atom separates
from CaCl and looses its negative charge, giving an increase
of the dipole again.
In order to simulate the infrared spectrum of the HCaCl
insertion complex, the dipole moment was calculated on a
relatively dense grid of 520 points in this region, defined in
the CaCl+ H product Jacobi coordinates. The distance
RCaCl−H was varied from 4.4 to 20a0 in 13 steps, the bond
length rCa−Cl from 4.369 to 7.369a0 in 8 steps, and the angle
␥ was given the values of 0°, 15°, 30°, 45°, 60°, and 90°. A
frame is used with its origin at the center of mass of the
complex, its z axis parallel to the Jacobi vector RCaCl−H, and
the Ca atom in the xz plane with x ⬎ 0. The electric dipole
surface in this region is represented by putting geometrydependent point charges on the nuclei. The components of
the dipole vector d can then be written as
dx =
FIG. 4. Magnitude of the electric dipole 共in a.u.兲 along the minimum-energy
reaction path of CaHCl calculated at the MRCI level. The path length was
computed from the distances between adjacent points, but contains an overall scale factor that is arbitrary.
harpoonlike reactions. Hence, the electric dipole moment expectation value over the MRCI wave functions was calculated in the regions of specific interest: along the minimumenergy reaction path, in the region of the Ca–HCl van der
Waals well, and in the region of the HCaCl insertion well.
Figure 4 shows the dipole moment along the minimumenergy path from reactants to products. In the Ca+ HCl and
CaCl+ H asymptotes it is very similar to the dipole of the
HCl and CaCl fragments, respectively, which possess strong
electric dipole moments. During the reaction the dipole
shows some interesting variations. First, in the region of the
saddle point it shows a maximum. Then, when the insertion
minimum is approached there is a sudden decrease of the
dipole and, subsequently, an increase when approaching the
product region.
These variations of the dipole from the saddle point to
the product region can be explained as follows. The increase
of the dipole when approaching the saddle point is related to
the ionic/covalent crossing. An electron jumps from Ca to
HCl; the resulting bent Ca+HCl− transition state complex has
a large dipole moment. The much smaller dipole of the
HCaCl insertion complex follows from the fact that the Ca
atom in this complex is a doubly charged cation and that
both the H and Cl atoms carry a single negative charge. The
opposite dipole moments of the HCa and CaCl fragments in
this H−Ca++Cl− complex very nearly cancel each other,
which gives a very small net dipole moment. The electronic
structure of HCaCl will be discussed below in more detail; it
can be understood by first considering the CaCl molecule.
The electronic structure of CaCl is well known:58,59 CaCl
consists essentially of an ionic Ca++Cl− core with a diffuse
rCl−Ca sin ␥
关mClQCa − mCaQCl兴,
mCa + mCl
rCl−Ca cos ␥
关mClQCa − mCaQCl兴
dz =
mCa + mCl
+
共6兲
RCaCl−H
关共mCa + mCl兲QH − mHQCa − mHQCl兴,
M
where ␥ is the angle between the two Jacobi vectors, M is
the total mass, and m␣ and Q␣ are the mass and effective
charge of atom ␣. With the aid of Eq. 共6兲 and the neutrality
condition QH + QCa + QCl = 0 the effective atomic charges can
be obtained from the calculated electric dipole moment.
The effective point charges were fitted to a series of
products of Rydberg polynomials of the same form as the
three-body terms in the potential 关see Eq. 共3兲兴. The rootmean-square errors in these fits were 0.09 and 0.15 D for the
x and z components, respectively. Figure 5 shows the geometry dependence of the electric dipole vector obtained from
the fit. In the same figure the fit of the ab initio computed
dipole function is compared with a dipole function obtained
with constant point charges QCa = + 34 , QCl = − 32 , and QH = − 32 .
In the region of the insertion well 共marked with dashed contours in the figure兲 the agreement is very good. Hence, the
assumption that the insertion well corresponds to an ionic
complex H−Ca++Cl− holds to a large extent, although not
completely. Figure 6, which shows the effective atomic
charges in the region around the insertion well, confirms this
picture.
Also, in the Ca–HCl van der Waals well the electric
dipole was calculated and fitted. Reactant Jacobi vectors
RHCl−Ca and rCl−H were used in this case. The distance
RHCl−Ca was varied from 8 to 15a0 in 10 steps, the bond
length rH−Cl from 2.01 to 3.01a0 in 6 steps, and the angle ␥
was given the values of 0°, 15°, 30°, 45°, and 60°, which
yields 300 points in total. The main contributions to the dipole function are the strong permanent dipole moment on
HCl and the weaker one induced by its electric field on the
Ca atom. The components of the dipole moment were fitted
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204307-9
Potential-energy surface for Ca+ HCl
FIG. 5. Electric dipole vectors in the region of the HCaCl insertion well.
Configurations where the potential energy is 7000 cm−1 above the bottom of
the well are marked by a dashed contour. Top panel: for r ⬅ rCl−Ca fixed at its
equilibrium value of 2.524 Å with R ⬅ RCaCl−H and ␥ being CaCl+ H product
Jacobi coordinates. Bottom panel: for R fixed at its equilibrium value of
3.245 Å. The solid arrows indicate the dipole from the fit, the dotted arrows
the constant effective charge model 共see text兲.
with the same kind of formulas as the interaction energy in
this region 关cf. Eq. 共5兲兴. Associated Legendre functions
Plm共␪兲 with m = 0 were used for dz and m = 1 for dx. The
result is shown in Fig. 7, in a body-fixed frame in which the
three atoms lie in the xz plane, with z parallel to RHCl−Ca.
J. Chem. Phys. 122, 204307 共2005兲
FIG. 6. Effective charges that fit the electric dipole moment 关see Eq. 共6兲兴 in
the region of the insertion well. Top panel: QCa, middle panel: QCl, and
bottom panel: QH. The CaCl-H product Jacobi coordinates are the same as in
Fig. 5.
excitation from a particular rovibrational level ⌽Jn, the initial
wave packet is constructed as ⌿t=0 = d · e⌽Jn, where d is the
dipole moment function and e is the electric polarization
vector of the incident light. In order to simulate a particular
J → J⬘ rovibrational transition the initial wave packet is pro-
V. SPECTRUM OF THE INSERTION COMPLEX
The deep insertion well can be inspected by infrared
spectroscopy; in this section we simulate the absorption
spectrum of the insertion complex. Two different methods
will be used for this purpose, and a body-fixed frame based
on product Jacobi coordinates.
First, we used a grid method that is very efficient to
compute excited states over a large range of energies, because it avoids an a priori choice of a basis set. Wave-packet
simulations were performed on a three-dimensional grid of
256⫻ 128 equidistant points for the radial coordinates
RCaCl−H and rCl−Ca, with 2 艋 R 艋 8 Å and 2 艋 r 艋 5 Å, and 50
Gauss–Legendre quadrature points for the angle ␥. Wigner
rotation matrices in terms of three Euler angles describe the
overall rotation of the complex. Details of the method can be
found in Ref. 60. In order to simulate infrared absorption by
FIG. 7. Electric dipole vectors in the region of the van der Waals well. The
HCl-Ca Jacobi coordinates are R ⬅ RHCl−Ca and ␪, while rH−Cl is fixed at its
equilibrium value of 1.2746 Å.
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J. Chem. Phys. 122, 204307 共2005兲
Verbockhaven et al.
204307-10
FIG. 8. Absorption spectrum of the HCaCl complex for J = 0 → 1 transitions
as a function of excitation energy simulated using the wave-packet method
described in the text. The J = 0 zero-point energy is 934.29 cm−1 with respect
to the bottom of the well at −16 852 cm−1.
jected on the J⬘ subspace60 by the application of an operator
PJ⬘ containing Wigner rotation matrices. The absorption
spectrum as a function of energy E is then obtained from the
Fourier transform of the autocorrelation function
␴共E兲 ⬀
=
1
Re
2␲ប
冕
⬁
0
exp共iEtប兲具⌿t兩PJ⬘兩⌿t=0典dt
兺 兩an⬘兩2␦共E − En⬘兲,
共7兲
n⬘
where an⬘ = 具⌽nJ⬘⬘兩PJ⬘兩⌿t=0典, while ⌽Jn⬘⬘ and En⬘ are the wave
functions and energies of the vibrationally excited states n⬘.
The evaluation of such an expression requires propagation
up to t = ⬁, in principle. In the present case the propagation
was continued for 6 ps, in steps of 1 fs, to scan a large energy
interval. Before the Fourier transform was performed the autocorrelation function was multiplied by an exponential
damping function exp共⌫t / ប兲 with parameter ⌫ = 3 cm−1, so
that the rhs of Eq. 共7兲 transforms into a sum of Lorentzian
functions of width ⌫. This value of ⌫ is smaller than the
energy separation of the excited states and all peaks in the
spectrum are fully resolved.
Figure 8 shows the spectrum thus simulated for the transition from the ground vibrational state with J = 0 towards all
final states with J⬘ = 1, as a function of the excitation energy.
The first peak at very low energy and not separately visible
in Fig. 8 corresponds to a pure rotational transition to the
ground level of J⬘ = 1, with ⍀, the projection of the total
angular momentum on the body-fixed z axis 共the CaCl–H
vector兲, equal to zero. The peak at 130 cm−1 corresponds to
the fundamental bend excitation with 兩⍀兩 = 1; it demonstrates
that perpendicular transitions are important. This state is a
50-50 mixture of basis functions with ⍀ = 1 and ⍀ = −1 with
definite parity under inversion of the spatial coordinates; it is
nearly degenerate with a similar level of opposite parity. The
weak peak at 259 cm−1 is the ⍀ = 0 component of the bend
overtone, while the peaks at 358 and 1271 cm−1 correspond
to the Ca–Cl and H–CaCl stretch motions, respectively.
There is no significant absorption intensity above
2000 cm−1. Similar results were obtained for a few other
initial vibrational states. This allows us to conclude that only
bound states up to this energy are required, i.e., ⬇30 states
for J = 0. The simulation of the spectrum corresponding to a
Boltzmann distribution at nonzero temperature would require
a series wave-packet calculations for each thermally occupied initial state ⌽Jn and final J⬘ = J − 1 , J , J + 1 according to
the dipole selection rules. Such a procedure is advantageous
only when very high excited vibrational states are involved.
In the present case it was more convenient to calculate all
relevant bound states directly.
The simulation of the infrared spectrum at different temperatures was performed by calculating all bound states up to
3000 cm−1 above the zero-point level, for J values up to 10,
inclusive. The method used is described in Ref. 14. The basis
consists of products of potential-optimized basis functions in
the radial coordinates RCaCl−H and rCl−Ca, associated with
Legendre functions in the angle ␥, and Wigner rotation functions for the overall rotation of the complex. The radial basis
functions are numerical eigenfunctions of one-dimensional
Hamiltonians with potentials obtained from the threedimensional global potential in the region of the insertion
well by freezing the two other coordinates at their equilibrium values. A centrifugal sudden approximation is used,
which decouples the calculations for different ⍀ values. This
approximation is justified by the linear structure of the
HCaCl insertion complex, which makes ⍀ a good quantum
number. Bound states were calculated for 兩⍀兩 = 0, 1, and 2. A
large basis of 16 800 functions, consisting of 50 Legendre
functions in ␥, 21 functions in R, and 16 functions in r, is
used for each J , ⍀. A nonorthogonal Lanczos iterative
method61 is used for the diagonalization.
The vibrational levels obtained from these calculations
can be represented fairly well by the usual linear triatomic
molecule expression
E共vr,vR, vb兲 = ␻r共vr +
1
2
兲 + ␻R共vR + 21 兲 + ␻b共vb + 1兲,
共8兲
where ␻r and ␻R are the fundamental frequencies of the
Ca–Cl and H–CaCl stretch vibrations, respectively, and ␻b is
the fundamental bend frequency. The symbols vr , vR , vb are
the corresponding quantum numbers; ⍀ runs from −vb to vb
in steps of 2 and J 艌 兩⍀兩. The results are ␻r = 355 cm−1, ␻R
= 1268 cm−1, and ␻b = 127 cm−1, in good agreement with the
results of the wave-packet calculations. The ground-state rotational constant B was extracted from the progression of the
lowest levels for J = 0, 1, etc. Off-diagonal Coriolis coupling
had to be included in order to obtain a realistic value of B.
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204307-11
J. Chem. Phys. 122, 204307 共2005兲
Potential-energy surface for Ca+ HCl
FIG. 9. Absorption spectrum of the HCaCl complex for different temperatures T. Homogeneous broadening parameter ⌫ = 1 cm−1.
The value of B = 0.13 cm−1 is close to that computed from
the equilibrium geometry.
The details of the calculation of the line strengths are
given in Ref. 14. Absorption intensities are computed from
these line strengths by averaging over a Boltzmann distribution of initial states. Figure 9 shows the absorption spectrum
simulated at different temperatures, with the assumption that
the lines are homogeneously broadened by Lorentzian functions of half-width at half maximum ⌫ = 1 cm−1. They agree
nicely with the T = 0 spectrum in Fig. 8. Detection of this
spectrum will provide a check on the accuracy of our computed potential surface in the region of the insertion well.
VI. CONCLUSION
We reported the global potential-energy surface of the
CaHCl system, describing the full reaction from
Ca共4s2 , 1S兲 + HCl reactants to CaCl共X 2⌺兲 + H products. This
surface is based on accurate ab initio calculations at the
MRCI level. The reaction is endothermic by approximately
5100 cm−1. There is a barrier of 4470 cm−1, arising from an
ionic/covalent crossing typical in harpoonlike reactions. The
transition state complex has a bent geometry. On each side of
this barrier is a well, a shallow van der Waals well in the
Ca+ HCl entrance channel, and a deep well corresponding to
a HCaCl insertion complex. Both the van der Waals complex
and the insertion complex have linear geometries.
Since the van der Waals well is important but is almost
two orders of magnitude less deep than the insertion well,
much attention was paid to the accurate computation of this
shallow well. Detailed CCSD共T兲 calculations showed that
the MRCI result for the van der Waals binding energy,
⬇190 cm−1, is underestimated by about 40 cm−1 共⬇30 cm−1
with respect to the CP corrected result兲. From a calculation
of the bound vibrational states in the van der Waals well of
the CCSD共T兲 and MRCI potentials it follows that the dissociation energies D0 differ by about 20 cm−1. A previous empirical estimate of the entrance channel well by de Castro–
Vítores et al.23 yielded a much higher binding energy, of
⬇980 cm−1, comprising a van der Waals contribution of
⬇200 cm−1, and a charge-transfer contribution of
⬇800 cm−1. The large charge-transfer term was probably introduced to explain the extraordinarily large binding energy
of ⬇1200± 400 cm−1 estimated by Menéndez et al.55 The
latter estimate used experimental photodissociation data with
the assumption that the recoil energy of the products could
be neglected. The much smaller binding energy from our
calculations shows that this assumption must be reconsidered.
Also, the electric dipole moment function of this system
was calculated. It provides valuable information about the
changes in the charge distribution along the reaction path.
The sudden increase of the dipole moment near the 共rather
late兲 transition state is due to a harpooning effect, and is
related to an avoided crossing between covalent and ionic
potentials. The dipole moment becomes much smaller at the
deep insertion well; this can be explained by a near cancellation of two oppositely directed dipoles in the H−Ca++Cl−
insertion complex. Finally, the dipole increases again to
reach the value of the CaCl product, which has an ionic
Ca++Cl− core with a diffuse outer electron.
The electric dipole function was also calculated in the
regions around the insertion and van der Waals wells and
fitted to analytical forms. It was found that a simple pointcharge model with nearly constant atomic charges nicely reproduces the dipole function in the region of the insertion
well. This model confirms the H−Ca++Cl− ionic picture of the
insertion complex.
Finally, rovibrational states were calculated in the insertion well and the infrared-absorption spectrum of the HCaCl
insertion complex was simulated, with the goal to facilitate
the experimental detection of this complex and establish the
accuracy of our potential-energy surface. Further work on
the dynamics of the Ca+ HCl→ CaCl+ H reaction on the
electronic ground- 共X兲 state potential-energy surface is in
progress.62
ACKNOWLEDGMENTS
We thank A. Aguado and M. Paniagua for interesting
discussions, for providing us with their programs, and for
advice on the fitting procedures. We thank P.E.S. Wormer for
critically reading the manuscript. This work has been supported by MCYT共Spain兲, under Grant No. BFM2001-2179,
and by the European Research Training Network THEONET
II.
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